Prove that `a^(2)+ b^(2) +c^(2) +2abclt2,` where a,b,c are the sides of triangle ABC such that `a+b+c=2.`

Let P be the point inside that Delta ABC. Such that angle APB=angle BPC=angle CPA. Prove that PA+ PB +PC =sqrt((a^(2)+b^(2)+ c^(2))/(2)+ 2sqrt3Delta,)where a,b,c Delta are the sides and the area of Delta ABC.

Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c) , where a,b,c gt 0 .

If sides of triangle ABC are a, b, and c such that 2b = a + c , then

Let a,b,c be the sides of a triangle ABC, a=2c,cos(A-C)+cos B=1. then the value of C is

If angle C of triangle ABC is 90^0, then prove that tanA+tanB=(c^2)/(a b) (where, a , b , c , are sides opposite to angles A , B , C , respectively).

If a,b and c are sides of a ritht triangle where c is the hypotenuse, prove that the radius of the circle which touches the sides of the triangle is r = (a + b-c)/(2).

If cos theta=a/(b+c), cos phi= b/(a+c) and cos psi=c/(a+b) where theta, phi, psi in (0, pi) and a,b,c are sides of triangle ABC then tan^2(theta/2)+tan^2(phi/2)+tan^2(psi/2)=

Prove that the area of an equilateral triangle is equal to (sqrt(3))/4a^2, where a is the side of the triangle. GIVEN : An equilateral triangle A B C such that A B=B C=C A=a . TO PROVE : a r(triangle A B C)=(sqrt(3))/4a^2 . CONSTRUCTION : Draw A D_|_B C .

If in a triangle ABC, (bc)/(2 cos A) = b^(2) + c^(2) - 2bc cos A then prove that the triangle must be isosceles.

Prove that a(b^(2) + c^(2)) cos A + b(c^(2) + a^(2)) cos B + c(a^(2) + b^(2)) cos C = 3abc